Relation To Independence
Random variables X, Y are independent if and only if the conditional distribution of Y given X is equal to the unconditional distribution of Y. For discrete random variables: P(Y = y | X = x) = P(Y = y) for all relevant x and y. For continuous random variables having a joint density: fY(y | X=x) = fY(y) for all relevant x and y.
Read more about this topic: Conditional Probability Distribution
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